{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.style.use(['seaborn-colorblind', 'seaborn-darkgrid'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d = {'A':[0, 0, 10, 0, 0], \n",
    "     'B':[0, 1, 8, 1, 0], \n",
    "     'C':[0, 2, 6, 2, 0], \n",
    "     'D':[1, 2, 4, 2, 1], \n",
    "     'E':[2, 2, 2, 2, 2]}\n",
    "p = pd.DataFrame(data=d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p_norm = p/p.sum(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A   -0.000000\n",
      "B    0.639032\n",
      "C    0.950271\n",
      "D    1.470808\n",
      "E    1.609438\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "def entropy(x):\n",
    "    y = []\n",
    "    for i in x:\n",
    "        if i == 0:\n",
    "            y.append(0)\n",
    "        else: \n",
    "            y.append(i*np.log(i))\n",
    "    h = -sum(y)\n",
    "    return h\n",
    "H = p_norm.apply(entropy, axis=0)\n",
    "print(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1aiFJn5pKit8htbodqDL27NmDmJgYzJ07FyYmJm8eQERERFTNCIKA8PBwtGz5AXbs+AlX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c3dee10>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 384
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ways = [1, 90, 1260, 37800, 113400]\n",
    "logwayspp = np.log(ways)/10\n",
    "plt.plot(logwayspp, H, 'o')\n",
    "plt.plot([0.0, max(logwayspp)], [0.0, max(H)],'--k')\n",
    "plt.ylabel('entropy', fontsize=14);\n",
    "plt.xlabel('log(ways) per pebble', fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0, 1.0, 1.0]\n"
     ]
    }
   ],
   "source": [
    "# Build list of the candidate distributions.\n",
    "p = [[1/4, 1/4, 1/4, 1/4], \n",
    "     [2/6, 1/6, 1/6, 2/6], \n",
    "     [1/6, 2/6, 2/6, 1/6], \n",
    "     [1/8, 4/8, 2/8, 1/8]]\n",
    "\n",
    "# Compute expected value of each. The sum of the multiplied entries is just a dot product.\n",
    "p_ev = [np.dot(i,[0, 1, 1, 2]) for i in p]\n",
    "print(p_ev)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.3862943611198906, 1.3296613488547582, 1.3296613488547582, 1.2130075659799042]\n"
     ]
    }
   ],
   "source": [
    "# Compute entropy of each distribution\n",
    "p_ent = [entropy(i) for i in p]\n",
    "print(p_ent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.09000000000000002, 0.21000000000000002, 0.21000000000000002, 0.48999999999999994]\n"
     ]
    }
   ],
   "source": [
    "p = 0.7\n",
    "A = [(1-p)**2, p*(1-p), (1-p)*p, p**2]\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.221728604109787"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-np.sum(A*np.log(A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sim_p(G=1.4):\n",
    "    x123 = np.random.uniform(size=3)\n",
    "    x4 = (G * np.sum(x123) - x123[1] - x123[2]) / (2 - G)\n",
    "    x1234 = np.concatenate((x123, [x4]))\n",
    "    z = np.sum(x1234)\n",
    "    p = x1234 / z\n",
    "    return - np.sum(p * np.log(p)), p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "H = []\n",
    "p = np.zeros((10**5, 4))\n",
    "for rep in range(10**5):\n",
    "    h, p_ = sim_p()\n",
    "    H.append(h)\n",
    "    p[rep] = p_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6++23tWfPHvXu3duU7w8AAHAmK3Yf0+Idae7xS1e2ksPODak4N4+cKjNr1ixP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\nIiJyAP8P68/i7mvP0+kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c69c240>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 375
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.kdeplot(H)\n",
    "plt.xlabel('Entropy', fontsize=14)\n",
    "plt.ylabel('Density', fontsize=14);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2217285264543143"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 9.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.08994119,  0.20996895,  0.21014867,  0.48994119])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p[np.argmax(H)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This notebook was createad on a computer x86_64 running   and using:\n",
      "Python 3.5.1\n",
      "IPython 6.2.1\n",
      "PyMC3 3.2\n",
      "NumPy 1.12.0\n",
      "Pandas 0.20.2\n",
      "SciPy 0.19.1\n",
      "Matplotlib 2.0.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import sys, IPython, scipy, matplotlib, platform\n",
    "print(\"This notebook was createad on a computer %s running %s and using:\\nPython %s\\nIPython %s\\nPyMC3 %s\\nNumPy %s\\nPandas %s\\nSciPy %s\\nMatplotlib %s\\n\" % (platform.machine(), ' '.join(platform.linux_distribution()[:2]), sys.version[:5], IPython.__version__, pm.__version__, np.__version__, pd.__version__, scipy.__version__, matplotlib.__version__))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
